1. Introduction

Theories in which quarks and leptons are treated in a unified manner often lead naturally to the speculation that there should exist interactions which violate baryon and lepton number. The rather stringent limit ( yr) on the proton lifetime suggests that such interactions, if present, must be mediated by very massive particles (with GeV). A null result in the forthcoming generation of searches for proton decay could rule out the detailed predictions of the present generation of models, but could never provide an ultimate proof for the absence of baryon number () violation. For further information on -violating interactions, one must forsake terrestrial experiments, and rely on indirect evidence from the early universe. According to the standard hot big bang model for the early universe, temperatures at sufficiently early times should have been high enough to overwhelm suppressions from large intermediate masses, rendering the rates for any -violating reactions comparable to those for -conserving ones.

If baryon number and the various lepton numbers were absolutely conserved by all possible interactions occurring in the early universe, then the total baryon and lepton numbers of the present universe must simply reflect their apparently arbitrarily imposed initial values. A plausible guess would be that the initial total baryon and lepton numbers were exactly zero (as the total electric charge appears to be). However, if this is to be viable some mechanism must exist which serves either to separate baryons and antibaryons or to hide antibaryons in the universe, since otherwise nearly all baryons should have annihilated away at temperatures above about 50 MeV in the early universe, and the present observed mean matter density, corresponding to would not be present. The fundamental prediction of models in which baryons and antibaryons are separated in the universe is the existence of antimatter galaxies. While there is quite convincing evidence against the presence of antimatter within our own galaxy (mostly based on the absence of obvious annihilation products), the constitution of other galaxies cannot definitely be ascertained. There is, however, an apparently insuperable theoretical difficulty with baryon-antibaryon symmetric models for the universe: the separation must have acted at times sec in order to prevent complete annihilation, but at these times the processes of separation cannot yet have acted over regions containing more than about particles ( since a light signal could not by that time have traversed a larger distance.

If -violating interactions do occur at very high energies, the present baryon number of the universe could no longer be specified simply as an initial condition. In fact, the presence of such interactions should serve to destroy all but perhaps a small fraction of any initial baryon number (see sect. 4), and insufficient baryons would have survived to explain the observed If no further effects occurred, then models involving appreciable B violation at very high energies would presumably be in disagreement with the standard cosmological model. However, if and invariances are also violated in -violating reactions, it is possible that a calculable baryon excess may be generated after any initial baryon excess has been erased, thus allowing large B violation at high temperatures without inconsistency with the standard hot big bang model of the early universe. Nevertheless, since invariance must remain intact, violation can have no effect unless a definite arrow of time is defined (see subsect. 2.1). In thermal equilibrium no preferred time direction exists. However, the expansion of the universe may result in small deviations from thermal equilibrium, which allow an excess of baryons over antibaryons to be generated by the action of -, -violating interactions. The relaxation time necessary to regain true equilibrium in which the baryon asymmetry has been destroyed again may increase faster than the age of the universe, thus freezing the asymmetry. A model along these basic lines was considered by Sakharov in 1966 [2], and since the development of grand unified gauge theories in which B violation is rampant, the generation of a baryon excess in the early universe has been discussed extensively [3,4,5,6,7,8]. In this paper we perform a detailed calculation of the development of a baryon excess in several simple illustrative models. Sect. 2 introduces the models, and derives Boltzmann equations for the time evolution of the number densities of the various particles involved. In sect. 3 we discuss the solution of these equations in the early universe, and find that for plausible choices of parameters, numerical solutions are obligatory. The final results depend sensitively on the parameters; the observed should therefore place interesting constraints on models for the very early universe and the interactions occurring in it. The final produced in any given model is always proportional to an unknown violation in super-high-energy interactions. The origin and magnitude of this violation is probably unconnected to that observed in the system. Nevertheless, since there is always an upper limit to -violating phases, any model involving violation which cannot generate sufficient even with maximal violation must presumably be considered in disagreement with the standard cosmology. The methods developed in this paper are easily generalized to an arbitrary model (see subsect. 2.4); in a forthcoming work we shall describe the constraints which result [29].

In grand unified models where the ``families'' are treated as simple replications of the lowest e family, it is inevitable that cosmological mechanisms which yield a net baryon number (and hence e number) in the universe should also generate net asymmetries of the same magnitude. Such an asymmetry in massless number densities would, however, be quite negligible and presumably unobservable. However, the same asymmetry should also exist for possible more massive absolutely stable replications (their masses are irrelevant if they are much smaller than the temperature GeV at which the asymmetries must be generated). The observed deceleration parameter for the universe suggests that the mean energy density does not exceed that observed in nucleons by more than about an order of magnitude. Thus there cannot exist absolutely stable particles much heavier than the proton in the concentrations suggested by grand unified models with the mechanism for baryon asymmetry generation described below. This constraint strengthens existing limits on neutral and charged heavy leptons and hadrons derived previously without grand unified models [13].

previous  l  next